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ECE 320: Session 3; Page 1/2 ECE 320: Lecture 3 Notes A. Homework #1 Passed Out B. ECE 321 Syllabus Passed Out Single Phase Power Calculations Power Factor • We can also define the Power Factor as pf = cos ( pf_angle) • Where (as a result of the limits on the pf_angle): 0 ≤ pf ≤ 1.0 • • • A lagging power factor means "I lags V". This is common with an R-L circuit. This means that the zero crossing for the current waveform appears after (to th right) the current zero for the voltage. A leading power factor means "I leads V". This is common with a series R-C circuit. This means that the zero crossing for the current waveform appears before (to the left) the current zero for the voltage. Unity power factor: "I in phase with V". pf = 0 MathCAD demo: See the other files associated with today's lecture Single Phase Instantaneous Power: v ( t) = Vm⋅ cos ( ω ⋅ t + φ v) i ( t) = Im⋅ cos ( ω ⋅ t + φ i) p ( t) = v ( t) ⋅ i ( t) p ( t) = Vm⋅ Im⋅ ( cos ( ωt + φ v) ⋅ cos ( ω ⋅ t + φ i) ) We can use the following Trig 2⋅ cos ( A) ⋅ cos ( B) = cos ( A − B) + cos ( A + B) ECE 320: Session 3; Page 2/2 Therefore we see: p ( t) = Vm⋅ Im ⋅ ( cos ( φ v − φ i) + cos ( 2ωt + φ v + φi 2 ) There is a constant term, that is commonly called the Average or Real Power Pave = Vm⋅ Im ⋅ ( cos ( φ v − φ i) ) 2 And a pulsating, double frequency term. This pulsating term causes vibration in single phase loads, and often audible noise. Note also that: Vm⋅ Im Vm Im = ⋅ = V ⋅ I 2 2 2 • If we have a black box with a current entering a box, and a voltage across the terminals, we need to determine whether it is a load (sinking power) or source (generating power). • If Pave>0 enters the box, then it is a load, if Pave<0 enters the box, it is a source. • Sometime electric machines are set up to regenerate, so they normally act as a load, but when one wants to slow to the rotation of the mechanical load, they can perform regenerative braking and transfer power in the other direction.